[en] Fatty acid composition influences the nutritional quality of milk and the technological properties of butter. Using a prediction of fatty acid (FA) contents by mid-infrared (MIR) spectrometry, a large amount of data concerning the FA profile in bovine milk was collected. The large number of records permitted consideration of more complex models than those used in previous studies. The aim of the current study was to estimate the effects of season and stage of lactation as well as genetic parameters of saturated (SAT) and monounsaturated (MONO) fatty acid contents in bovine milk and milk fat, and the ratio of SAT to unsaturated fatty acids (UNSAT) that reflect the hardness of butter (SAT:UNSAT), using 7 multiple-trait, random-regression test-day models. The relationship between these FA traits with common production traits was also studied. The data set contained 100,841 test-day records of 11,626 Holstein primiparous cows. The seasonal effect was studied based on unadjusted means. These results confirmed that milk fat produced during spring and summer had greater UNSAT content compared with winter (63.13 vs. 68.94% of SAT in fat, on average). The effect of stage of lactation on FA profile was studied using the same methodology. Holstein cows in early first lactation produced a lower content of SAT in their milk fat. Variance components were estimated using a Bayesian method via Gibbs sampling. Heritability of SAT in milk (0.42) was greater than heritability of SAT in milk fat (0.24). Estimates of heritability for MONO were also different in milk and fat (0.14 vs. 0.27). Heritability of SAT:UNSAT was moderate (0.27). For all of these traits, the heritability estimates and the genetic and phenotypic correlations varied through the lactation.